Ignore everything I said before. Even though changing the password fixed the problem for a little while, the next morning I was back to seeing "Authentication Error" and fluctuating signal strength for the wireless networks on the tablet.
Walking through the living room a little later, I noticed some lights blinking near the floor. It was a Wireless-N extended that I had installed a while back. I had forgotten about it. I unplugged it and ... ta da! ... the wireless connection between my new router and the Samsung tablet is working.
Edit: But, it is displaying signal strengths that are much lower than other devices in the same location are reporting.
-- Roger